The present invention relates to methods and tools for identifying vortices within a fluid flow.
The understanding of vortices/recirculations within fluid flows is an important engineering consideration, particularly, although not exclusively in the design of components or assemblies that are intended to interact with a fluid flow in use, i.e. so-called ‘fluid-washed’ components. This is especially the case for aerodynamic components, such as aerofoils, for which the efficiency of operation is dependent upon the manner in which the component affects the adjacent/surrounding fluid flow.
It is an engineering aim to be able to locate vortices accurately. The presence of a vortex on or adjacent a surface of a fluid-washed component can reduce aerodynamic efficiency and potentially cause other abnormal machine behaviour or even failure. Whilst it is possible to test physical components and flow regimes using conventional equipment such as wind tunnels and the like, there is a general trend, as in other areas of engineering, towards the use of computational modelling of fluid flow. Such computational techniques allow a deeper understanding/analysis of flow regimes and also allow changes to designs and test conditions to be implemented quickly and cost-effectively, thereby increasing the ability to experiment with alterations.
The inventor has assessed a number of different computational techniques for identifying vortices in a fluid flow as identified below:
Graphical Visualization of Vortical Flows by Means of Helicity (Y. Levy, D. Degani, and A. Seginer. AIAA J., 28(8):1347-1352, 1990) suggests identifying vortices using helacity, which is defined as the cosine of the angle between velocity v and vorticity w. The underlying assumption of the algorithm is that, near vortex core regions, the angle between v and w is small, which corresponds to a big helicity value. The detection algorithm locates points with maximum helicity values and traces streamlines from these maximum points.
Education of Swirling Structure using the Velocity Gradient Tensor (C. H. Berdahl and D. S. Thompson. AIAA J., 31(1):97-103, 1993) defines a swirl parameter τ based on the existence of complex eigenvalues in velocity gradient tensor J, as given by the following equation:
      τ    =                                                  Im            ⁡                          (                              λ                C                            )                                                ⁢        L                    2        ⁢        π        ⁢                                        v            conv                                          ,where Im(λC) is the imaginary part of the complex conjugate pair of eigenvalues of J, L is the characteristic length associated with the size of the region of complex eigenvalues RC, and vconv is the convection velocity aligned along L. The basic idea of the detection algorithm is that, τ is non-zero in regions containing vortices and achieves a local maximum at vortex core.
On the Identification of a Vortex (J. Jeong and F. Hussain. J. Fluid Mechanics, 285:69-94, 1995), the velocity gradient tensor J is decomposed into its symmetric part S, and its anti-symmetric part Ω. That is, S=(J+JT)/2; and Ω=(J−JT)/2. The vortex is defined as a connected region where two of the three (real) eigenvalues of the symmetric matrix (S2+Ω2) are negative. Thus, if the second highest eigenvalue λ2 of (S2+Ω2) is negative at a point, then the point belongs to a vortex.
A Predictor-Corrector Technique for Visualizing Unsteady Flow (D. C. Banks and B. A. Singer. IEEE Trans. Visualization and Computer Graphics, 1(2): 151-163, 1995) defines vorticity ω as the curl of velocity v, which represents local flow rotation in terms of both speed and direction. This technique requires that vortices are sustained by pressure gradients and indicated by vorticity. Therefore, the algorithm detects vortex core lines by tracing vorticity lines (seeded with points that are of low pressure and high vorticity magnitude) and then correcting the detected lines based on local pressure minimum.
Identification of Swirling Flow in 3D Vector Fields (D. Sujudi and R. Haimes. In AIAA 12th CFD conf., Paper 95-1715, 1995) uses an eigenvector method, the underlying assumption being that the eigenvalues and eigenvectors of the velocity gradient tensor J, evaluated at a critical point, define the local flow pattern about that point. The algorithm thus searches for points where J has one real and two complex conjugate eigenvalues. If the eigenvector of the real eigenvalue is parallel to the velocity vector, then the point is determined to be part of the vortex core.
A Higher-Order Method for Finding Vortex Core Lines (M. Roth and R. Peikert. In IEEE Visualization '98, pages 143-150, 1998) uses higher-order derivatives of velocity v to detect vortex core lines. It is observed that the eigenvector method is equivalent to finding points of zero torsion. Thus, the second-order derivative w of v is computed and a vortex core line consists of the points where v is parallel to w.
Computer Visualization of Vortex Wake Systems (R. C. Strawn, D. N. Kenwright, and J. Ahmad. AIAA J., 37(4):511-512, 1999) defines a vortex core as being a local maximum of vorticity magnitude |ω| in the plane normal to ω. This method is designed specifically to detect multiple vortices in close proximity with the same orientation and overlapping cores.
The above-described techniques share a common theme that the definition of a vortex is based upon each author's own specific understanding or observation of what properties constitute, and therefore define, a vortex. Such diverse vortex definitions leave open the possibility that any one definition could identify or overlook a vortex where another definition does not. Accordingly, the prior art techniques are subjective in nature.
For most of the prior art techniques, there exists a problem that false positive vortex identifications are generated, i.e. where detected core lines or regions do not actually contain vortices. This can thus lead to errors or else an increase in post-processing efforts in order to verify the correctness of detected vortices by either manual visualization or designing feature verification algorithms, the verification accuracy of which may also be uncertain.
Some techniques can also generate false negatives, where vortices do exist but are not detected. The false negative problem is difficult to guard against since it is not straightforward to identify where or why vortices are missing using conventional techniques.
Furthermore, some of the techniques require users to specify thresholds for algorithm parameters in order to achieve best performance of the algorithms and, accordingly, there is margin for significant error due to the level of skill of the operator. Even for a skilled operator, it is not a straightforward task to ascertain the best thresholds and so another vortex detection technique may need to be used in order to validate/check the generated results.
It is an aim of the present invention to provide for vortex identification in a manner that substantially avoids or mitigates one or more of the above problems. It may be considered an aim of the invention to provide a more effective or objective vortex identification technique.